高自旋 Clifford 分析中的玻色子拉普拉斯算子
Bosonic Laplacians in higher spin Clifford analysis
AI总结：
本文推广经典 Clifford 分析至高自旋情形，引入二阶共形不变的玻色子拉普拉斯算子，揭示其与麦克斯韦方程的联系，并提出简化与 Rarita-Schwinger 型算子关联的新定义及矩阵型算子。
摘要：
在本文中，我们首先引入高自旋 Clifford 分析，它通过考虑取值于自旋群的不可约表示的函数，被视为经典 Clifford 分析的推广。然后，我们在高自旋 Clifford 分析中引入一类二阶共形不变微分算子，称为玻色子拉普拉斯算子。特别地，我们将展示它们与经典麦克斯韦方程组的密切联系。最后，我们将引入一种定义玻色子拉普拉斯算子的新视角，这简化了之前获得的玻色子拉普拉斯算子与 Rarita-Schwinger 型算子之间的联系。此外，我们获得了一个矩阵型 Rarita-Schwinger 算子，并提供了与这个新的一阶矩阵型算子相关的一些结果。
英文摘要：
In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we introduce a type of second order conformally invariant differential operators, named as bosonic Laplacians, in the higher spin Clifford analysis. In particular, we will show their close connections to classical Maxwell equations. At the end, we will introduce a new perspective to define bosonic Laplacians, which simplifies the connection between bosonic Laplacians and Rarita-Schwinger type operators obtained before. Moreover, a matrix type Rarita-Schwinger operator is obtained and some results related to this new first order matrix type operator are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
